International Journal of Applied Electromagnetics and Mechanics

Preface to the ISTET '01 special issue.

The application of network-oriented methods to electromagnetic field problems can contribute significantly to the problem formulation and solution methodology. The field problem can be systematically treated by the segmentation technique and by specifying canonical Foster representations for the subcircuits. Connection between different subdomains is obtained by selecting the appropriate independent field quantities via Tellegen's theorem. For each subdomain, as well as for the entire circuit, an equivalent circuit extraction procedure is feasible, either in closed form for subdomains amenable of analytical description or via the relevant pole structure description when a numerical solution is available.

Network concepts in electromagnetics motivate and faciltate the application of complexity reduction methods to the state equations describing the discretized electromagnetic field. Two general approaches toward such reduction are reviewed in this paper. The first involves the application of model order reduction methodologies in the context of the state space representation of the discrete electromagnetic model. The second considers the application of system identification and parameter estimation methods for reduction of computational time and automatic generation of lumped element equivalent circuits.

This article describes the influence of gaps on the shielding performance of a box. The investigation has been carried out with the Finite Element Method and especially a method with adaptive mesh generation.

The plane transient eddy current problem of a system of N arbitrary conductors with different magnetic permeability is solved in the time domain by time-separation. This leads to an eigenvalue problem which we treat by evaluating several volume and boundary integral equations for the vector potential. It is shown that the eigenfunctions of the different integral equations form complete orthogonal systems. As examples of application we calculate the transient behavior of the conductor system after connecting it to sources of direct voltage or direct current at time t=0.

An advanced numerical calculation scheme based on finite and boundary elements as well as multigrid methods is presented. This scheme is used for the precise forecast of the dynamical behavior of piezoelectric, electrostatic and, magnetomechanical devices, especially sensors and actuators. Application examples include solenoid valves, piezoelectric source for the generation of acoustic shock waves, magnetic surface acoustic wave (SAW) filters, electrodynamic loudspeakers and magnetostrictive tool actuators.

Computing the capacitance coefficients of a multiconductor system embedded in multiple piecewise homogeneous dielectrics with the boundary element method in combination with the fast multipole method, the memory requirements and the computational cost for the solution of the system of linear equations are approximately proportional to the number of unknowns. In this paper it will be shown, that the calculation of the free charges on the conductors and with it the calculation of the capacitance coefficients can be accelerated, if the fast multipole method is also used for the post-processing.

In this paper the design of linear multivariable control systems based on the l_{1} - system norm is revised. It is shown how the well known computational difficulties inherent in this design problem can be overcome. For this purpose a procedure is proposed consisting of the steps 1) design of a suitable low order controller by semidefinite programming, 2) parametrization of all stabilizing conrollers based on the controller of the first step, 3) solution of the design problem with linear programming methods. The efficiency of this method is demonstrated by an example.

This paper addresses the problem of global robust positivity for polynomials with coefficients depending linearly on uncertain parameters. Based on considerations from real algebraic geometry, numerical LMI solvers and the theorem of Ehlich and Zeller we propose two algorithms for the estimation of the convex region in the space of coefficients, for which a polynomial is globally positive. Illustrative examples are given.

This contribution presents tests, based on Lie-groups, for the accessibility and the observability of dynamic systems described by a set of implicit ordinary differential equations. It is shown that non-accessible or non-observable systems admit Lie-groups acting on their solutions such that distinguished parts of the system remain unchanged. The approach being presented requires the formal integrability of the system. Therefore, a short introduction to this theory is presented, as well as its application to systems of differential equations. Besides the theoretical results sketches for computer algebra based algorithms are presented that are necessary to perform the test for higher order systems.

Algorithms for the modeling of waveguide circuits are described. The material parameters can be anisotropic. Starting with generalized transmission line equations, suitable expressions for the analysis are derived. The introduction of the admittance/impedance transformation concept guarantees numerical stable expressions even in case of long devices or high numbers of concatenated sections. The presented algorithm is validated by comparing numerical results with those obtained by measurement and other numerical methods.

This paper presents a generalized transmission-line theory which is useful to describe the wave propagation along almost arbitrary three-dimensional wire structures. In contrast to the classical transmission-line theory this new approach is an approximate full-wave description based on generalized telegrapher's equations. Whereas the mathematical structure of the classical telegrapher's equations is preserved, the coefficients (the per-unit-length parameters) are generalized in order to represent the intrinsic behavior of the wire structure. MoM simulations were performed to validate the predicted data.

An approach for modeling wave propagation in graded index waveguides within the validity range of geometrical optics is presented. The method is based on wavefront construction in conjunction with dynamic ray tracing, which are both well known for seismic applications. The objective of this paper is to apply this formulation to the analysis of wave propagation in highly multimode optical waveguides whose index changes are small within the scale of a few wavelengths of the guided light and whose lengths are very large compared to the wavelength. In addition the method is applied to bulk optical components like the Luneburg lens.

In this paper, we present a detailed mathematical analysis of nonlinear resistive networks with multiple dc-operating points. In our approach, we use elementary set theoretical principles of network theory. We propose two new approaches: the TC-method (transfer-characteristic method) and the DPC-method (driving-point characteristic method). We use the TC-method to reduce the computation of dc-operating points of a given nonlinear resistive network to the computation of crossing points between transfer characteristics of associated modified resistive networks with a straight line. It can be proved that at least one operating point of the given network corresponds to each such crossing point. We show that the proposed approaches lead to continuation methods for the finding dc-operating points of resistive networks. These continuation methods can be readily used in standard SPICE-like circuit simulators.

In several applications a symbolic description of nonlinear electrical networks is of great importance. Thus, this paper is concerned with the systematic derivation of the mathematical models of a certain class of nonlinear electrical networks in view of an efficient computeralgebra implementation. The approach being proposed is based on a modified version of the famous equations of Brayton-Moser in combination with the so-called state-tree representation. The network algorithms are implemented in an object-oriented package in the computeralgebra program Maple and they have been tested for several nontrivial examples.

Stimulated by recent work on the synthesis of a certain class of surface acoustic wave (SAW) filters, we discuss the exceedingly classical subject of physical realizability criteria for lossless, and reciprocal linear multiports. We give an essentially coordinate-free formulation of the realizability conditions for passive, lossless and reciprocal multiports. For this sake we describe a linear multiport by its external behavior (the linear subspace generated by all admissible signal pairs at the ports) and analyze the properties of this space in terms of Gramians of its bases with respect to physically relevant metrics. The standard matrix representations (impedance matrix, scattering matrix, …) arise by the introduction of various affine coordinates in the external behavior. Instead of discussing their well-known coordinate-dependent properties we focus on the so called P-matrix as an attractive non-standard example and study its properties and relations to other matrix representations. As a major result we show that the parameterization of lossless multiports as induced by the P-matrix is largely equivalent to the Arov-Dewilde-Dym parameterization of J-inner functions.

The paper describes an approach to general-purpose design sensitivity analysis for electromagnetic devices. Microsystem technology often requires the assessment of manufacturing techniques or effects of tolerances. Emphasis is therefore put on the adaptability to different requirements, depending on desired accuracy, computational effort and significance. By introducing a distributed sensitivity function, the effect of small contour distortions can be described. The design sensitivity is based on a magnetic double-layer model. It is shown that sensitivity can be expressed in terms of virtual anti-parallel double-layer currents, flowing in a movable contour. The sensitivity is explicitly derived for two-dimensional coordinate systems using the finite-difference method within a commercially available field computation program. The proposed method is demonstrated by two examples.

In general, if measurements can be repeated several times assuming the same conditions, the measurement error can significantly be decreased by statistically evaluating the measurements. However, an uncertainty band always remains. Non-linear numerical simulations based on e.g. the Newton-Raphson method may establish a poor convergence if they are provided directly with measured data. Therefore, data pre-processing is required. Here, a neural network approach is employed. A two-layer perceptron is fitted on a measured magnetisation curve, thereby restricting the solution to be technically feasible while accepting the statistical nature of the data. By using a perceptron, an analytical expression of the magnetisation curve is obtained and expressions for its derivatives can easily be computed.

The nonlinear computations based on the Newton-Raphson algorithm may suffer poor convergence provided that the measured data are employed directly. The aim of this work is to present the method to improve convergence rate of magnetic field simulations taking hysteresis into account. The Preisach model is considered. It is proposed to use the neural network approximator to obtain smooth hysteresis model output. The mathematical representation of the neural network is exploited to obtain analytical expression for derivative of the hysteresis model output. Moreover, taking advantage of the analytical form of the Preisach function, it is shown that speed up in calculations of hysteresis energy losses can be achieved.

In the present paper the concept of dynamic shape control of structures is addressed. The term "shape control", not to be confused with automatic control, means to identify the spatial distribution (or shape) of an actuating control agency, such that a structural displacement field with a desired spatial distribution (or shape) is reached. This field aspect requires a spatially distributed control actuation, which, in the present paper, is performed by means of assigned piezoelectric eigenstrains. The goal of our proposed dynamic shape control procedure is to shape the piezoelectric actuation such as to obtain a displacement field coinciding with a dynamic displacement field induced by external forces. Equivalently, we may eliminate the force induced dynamic displacements. Bending vibrations of straight composite piezoelectric beams are studied in more detail. First, the coupled electro-mechanical field equations are developed and then the dynamic shape control problem is solved in closed form for this coupled formulation. It turns out that exact elimination of force induced vibrations is possible when the shape of the piezoelectric actuation coincides with a statically admissible bending moment distribution of the force loaded beam. Distributions characterizing non-unique solutions are discussed, and aspects of collocated sensing are addressed.